Tuesday, November 30, 2010

One thing that Judith Curry's blog has done is attract a number of newbies (well, at least new to Eli) with a number of questions that have simple answers once Eli takes a few days to think about them. It's not that your average climate blogging bunny does not know the answer, but rather that the explanation has to be on a level that the naive skeptic can grok. Grokking for anyone born after 1970 is understanding something at a soul deep level.

I can’t believe that IR absorbtion directly heats the air, for it’s pretty transparent and close to an ideal gas.

Yet, Curryja wrote…………. “Then through the equipartition of energy, the absorption of radiation causes the molecule to move faster and bump into the other molecules like N2, O2, and make them move faster. …”

My “built-in-doubter” is triggered.

Absorption of a photon I thought merely bumped an electron from one orbital shell to another, raising the molecule’s potential energy not its kinetic (temperature). Just as winding a clock tightens its mainspring instead of warming the mechanism. That’s why there’s spectrometer lines…….

Well, that energy is released later by re-radiating another photon when the electron returns to its natural orbit

There are important, in the sense that many have them, misconceptions here. First that the atmosphere is transparent in the IR. The atmosphere is transparent in the visible, but, there are many regions of the IR where absorption is high, including those regions where CO2 and H2O absorb. A handy dandy number to carry about is that at the surface the average distance light can travel in the CO2 spectral region is 10 meters (or about 35 feet for you unethical customary unit users).

The second is the impression that the energy stays in the molecule that absorbs it, to be re-radiated later. This is not so, it is quickly degenerated to thermal motion (translation, zipping about) via collisions. This process is called thermalization and requires about a microsecond at atmospheric pressure. So where does the emission come from the bunnies ask?

Well, there is a considerable amount of thermal energy at room temperature, and even much lower. True this average energy is low compared to even the lowest vibrational excitation of CO2 (which would be ~1000 K), but it is enough that a small, but significant fraction of the CO2 molecules are excited to levels which can emit in the IR (about 6% at room temperature).

A third often stated misconception is that CO2 is such a small fraction of the atmosphere that it cannot absorb or maintain any significant amount of energy. This is where Eli the wonder bunny has thought of a great answer:

Think of CO2 as a turnstile through which energy passes from the ground to the atmosphere. A large crowd can pass through a few turnstiles.

UPDATE: Upon reflection (and a pointed comment by one who does not wish to be named, always welcome at RR), this is even better than Eli thought. Having to go through turnstiles slows up rushing crowds. If the CO2 is playing the role of a turnstile, and the poor innocent photons have to get through a series of them it will really slow up the rate of emission to space.

Curry is now trying to explain the GHE but seems to think the scientific explanation involves greenhouses. Oh dear. She is the slow person butting in on an ongoing conversation and continually say "eh? what was that?"

(a) When the photon is absorbed the entire atom moves, because of conservation of momentum.

(b) After the absorption of the photon, it is quite common for an atom to hit another one while it is still in the excited state. This results in the two atoms recoiling from each other and no emission of a photon. That's why there's actual absorption and not just reradiation.

In general the different modes (photon and motion) are well-coupled and energy will exchange from one to the other.

In so far as I am taking the first semester of a general chemistry sequence, and we are curently covering atomic structure and light absorption & emision this student has a question. You state that:

the impression (is) that the energy stays in the molecule that absorbs it, to be re-radiated later. This is not so, it is quickly degenerated to thermal motion (translation, zipping about) via collisions. This process is called thermalization and requires about a microsecond at atmospheric pressure.

Could you expand upon how this is thought to work?

On the whole chemistry students are introduced to a number of ideas, concerning light absorption and emmision, with which to work. What I have not come to yet is an overall understanding of what the relationship is amongst the various ideas. For example, how do the frequencies at which light is emited by an atom with an excited electron relate to its absorption characteristics. The example which is given for emission (in my text which is Kotz, Treichel & Townsend "Chemistry and Chemical Reactivity") are gases which have been super heated so that they emit light which can be split into component frequencies by a prism. The radiative behavior which is the subject of our discussion does not seem to happen at extraordinary temperatures. The question is what is happening. How do we go from absorption of a photon to motion. Perhaps this is not a useful question.

Mitch, the momentum transfer on absorption or emission of a photon is really small, a part in 10^4 for visible light, proportionally less for IR. this amounts to cm/sec, when the thermal velocity of the atom is 10^4 cm/sec. In other words for this case it can be neglected, but not for very cold gases such as Bose-Einstein condensates.

Your second point is somewhat semantic, however one can differentiate scattering from absorption by how long the molecule/atom stays in the excited state. On that basis Raman is scattering and fluorescence is emission.

Folks:The longwave IR radiation does not disturb the electrons at all. The photons are not energetic enough to kick an electron to a higher state. That's why atomic emissions are in the visible and ultraviolet, not LWIR. LWIR photons bend and stretch the bonds between the atoms of polyatomic molecules, which is why the main greenhouse gases are things like CO2, H2O, O3, and CH4. The vibrating molecules transfer their vibration energy into kinetic energy, meaning temperature, on a time scale much shorter than the time it would take to reradiate as LWIR. So absorbed LWIR goes straight to raising the local temperature. That's it. The thermal energy can be removed in various ways - evaporating water, melting ice, being carried elsewhere by convection, etc. Some will be reradiated as LWIR. Half of that goes up, and half goes down.

Clearscience, you are making the mistake of thinking Judy ever was a climate scientist. Her expertise was in tropical storms--really a different beast. There is no more reason for her to comprehend the greenhouse effect than for you or I to. If we've studied it and she hasn't, it is unlikely she'll appreciate the more subtle aspects--and there are subtleties.

I have to agree with Paul Mouse. I thought the IR radiation was absorbed into the slightly polar bonds of carbon dioxide, water vapor, methane and other greenhouse gases. The IR wavelengths excite the molecular bonds and causes the molecule to vibrate (imagine the molecules vibrating where the atoms in the molecule are attached to other by springs). The vibrating molecule ends up with a higher kinetic energy, not potential energy (as the description above implies).

When these higher kinetic energy molecules collide with other molecules (which in air are most likely nitrogen or oxygen gas molecules), they impart some of this kinetic energy to these diatomic gas molecules. This raises the kinetic energy of the air, and then as result of huge numbers of collisions, raises the temperature as the kinetic energy is converted to thermal energy. A small number of molecules get excited enough due to the random molecular collisions to emit a photon of infrared, thus completing the cycle from infrared radiative energy to kinetic energy to thermal energy and back to infrared radiative energy.

The number of molecules that get excited enough to emit IR is consistent with the Stefan-Boltzman law, which states that the radiation should be proportional to the absolute temperature to the fourth power; i.e. based primarily on the absolute temperature of the air. So the IR radiation emitted by the air can come from any of the molecules in the gas, not just the GHG molecules.

I am just a chemical engineer, so I hope I didn't mess this up too bad for the physicists to explain more accurately. I guess some discerning physicist will correct me, and tell me that the 'excited molecular bonds' have something to do with higher electron energy states, so I welcome corrections by someone more knowledgeable than myself.

Patrick, it is actually an excellent set of questions and one that one of my students asked today. =:0 Unfortunately a complete answer requires at least two courses in quantum mechanics, but allow Eli to sketch one out.

Molecules have quantum states just as atoms do. In general we can divide these states into overlapping rotational, vibrational and electronic levels. (Atoms only have electronic states). Each electronic level (corresponding to arrangement of the electrons in molecular orbitals) has many vibrational substates (roughly ways in which the nuclei move relative to each other), and each vibrational substate has an array of rotational levels (the whole molecule swings in space). To first order these modes of motion are decoupled from each other. To second order. . . ah there are tigers there.

There are selection rules which govern when a molecule in a particular state can absorb or emit a photon. The first rule is that the energy of the photon exactly match the energy difference between the two states. There are many other selection rules, you start to learn these in physical chemistry.

Whether a molecule absorbs or emits the matching photon depends on which state the molecule is in. If it is in the lower state, it absorbs, if it is in the upper state it emits either a spontaneous or stimulated (laser) manner. The reason for heating the molecules in a discharge is to move atoms/molecules into the upper state from which they can emit. The pictures in the texts are usually a result of electric discharges, where the excitation comes from electron collisions (think neon signs).

Molecules interact with each other via electromagnetic fields. In GChem we introduce ions, dipoles (asymmetric arrangement of charges in a molecules) and induced dipoles (somewhere around chapter 10 in your text book, look up London forces in the index). An ion/molecule interacts with others through electromagnetic forces. The range of these forces varies considerably, ion - ion is strongest, induced dipole - induced dipole weakest and, of course there is everything in between.

What we mean by a collision is that two molecule approach closely enough that their energy levels are shifted enough to overlap neighboring levels. In such a case you can have a transition from one state to the other consistent with conservation of energy and momentum.

Zinfan, a harmonic oscillator has both potential and kinetic energy. For a quantum oscillator, only the total energy is fixed. In terms of collisions, the interaction between molecules is determined by the overall distribution of charge (for CO2 an induced dipole).

While vibration is thought of as a motion of the nuclei, in this discussion you cannot loose track of the electrons forming the bonds between them.

I think the model proposed here is meaningful, though I think there are still some issues.

If most of the energy absorbed by GHG's is thermalized through collisions with mostly homonuclear diatomic molecules (N2 and O2), how is the radiation flux at the top of the atmosphere maintained? That is, as homonuclear diatomic molecules, N2 and O2 CANNOT emit radiation when they are excited to higher lying vibrational and rotational states because those molecules don't have a permanent dipole moment.

So how does the net flux of radiation stay the same (within our ability to measure the net flux at least) if most of the molecules that end up energetically excited cannot emit radiation toward the top of the atmosphere?

Also,

'...however one can differentiate scattering from absorption by how long the molecule/atom stays in the excited state. On that basis Raman is scattering and fluorescence is emission.'

is a convoluted statement and doesn't really clear up any ideas presented here. In the case of spontaneous, non-resonant Raman scattering, which would dominate in the atmosphere, time doesn't really exist. Both time-ordered terms in the molecular polarizability contribute to the overall effect. From the most rigorous perspective, there isn't any amount of time that the molecule spends in the excited state. The light 'scatters' from the molecule.

The point Mitch is getting, albeit runabout, is that the surroundings of a excited molecule will greatly affect the lifetime of an excited state before spontaneous emission occurs. The stronger the interaction with its surroundings, the shorter the amount of time the molecule will spend in its excited state before emitting an allowed photon. Excited state lifetimes (both electronic and vibrational) get exceedingly short in condensed phases.

Inelastic light scattering is neither here nor there in that discussion.

From Eli's essay, "There are important, in the sense that many have them, misconceptions here. First that the atmosphere is transparent in the IR. The atmosphere is transparent in the visible, but, there are many regions of the IR where absorption is high, including those regions where CO2 and H2O absorb. A handy dandy number to carry about is that at the surface the average distance light can travel in the CO2 spectral region is 10 meters (or about 35 feet for you unethical customary unit users)."

What I use is the example of a microwave oven. Water is transparent to light, but clearly it isn't transparent to at least some microwaves, and greenhouse gases operate on exactly the same principle. Given the electric dipole of the molecule and its natural (quantized) frequency of vibration it is able to absorb and emit radiation in the form of photons assuming the electromagnetic field includes waves of roughly the same frequency. Then once the energy has been absorbed it is generally lost due to collisions with other molecules.

Anyway, don't know if it is at a level that people can grock, but I deal with many of the issues -- and will be bringing more in over time, as well as the visuals and the history here:

And I will be doing other pages in the same style as well. Central essay, then little supporting miniatures with links all as part of a dynamic, multimedia hypertextual webpage. Not necessarily for that sort of "skeptic" but some should find it helpful -- and it will give them the chance to go into it in as much depth as they like -- for a little bit, at least.

"Infrared photons will be absorbed by CO2 in that band. The greater the concentration the greater the absorption. The energy is quickly lost in collisions, mostly with nitrogen and oxygen. In a nitrogen or oxygen pair both atoms have the same net charge and neither are capable of absorbing or emitting the radiation and are invisible to it. But with absorption by greenhouse gasses the atmosphere warms just as food in a microwave oven -- given the absorption of microwave radiation by water molecules."

Maxwell wrote: "So how does the net flux of radiation stay the same (within our ability to measure the net flux at least) if most of the molecules that end up energetically excited cannot emit radiation toward the top of the atmosphere?"

I believe what you are looking for is the "Planck feedback." Putting greenhouse gases into the atmosphere reduces the rate at which energy leaves the system but the rate at which radiation enters the system remains roughly the same, therefore the amount of thermal energy in the system rises. This increases the rate at which molecules radiate thermal energy with the rate being proportional to the temperature taken to the fourth power in accordance with the Stefan-Boltzmann law.

The temperature -- and thus the rate at which thermal radiation is radiated -- will continue to rise until the rate at which energy enters the system is balanced by the rate at which energy escapes the system. Radiation balance theory -- with Planck feedback as a negative feedback.

"The satellite image demonstrates that just as increasing the levels of CO2 in a tube within a laboratory reduces the amount thermal radiation that is able to make it from one end of the tube to the other, increasing the levels of CO2 in the atmosphere reduces the rate at which radiation escapes to space. Now if you reduce the rate at which radiation escapes to space but keep the rate at which radiation enters the system the same then energy must accumulate in the climate system. This follows from the principle of the conservation of energy, and this is what raises the average temperature of the globe. And the temperature will keep on rising until the increased infrared luminosity compensates for the increased concentrations of CO2 in the atmosphere -- so that the rate at which energy leaves the system is equal to the rate at which energy enters the system."

*

Maxwell wrote: "The point Mitch is getting, albeit runabout, is that the surroundings of a excited molecule will greatly affect the lifetime of an excited state before spontaneous emission occurs. The stronger the interaction with its surroundings, the shorter the amount of time the molecule will spend in its excited state before emitting an allowed photon. Excited state lifetimes (both electronic and vibrational) get exceedingly short in condensed phases."

"At a given temperature collisions will also maintain a certain percentage of molecules in an excited state at any given time, thus over a given period a certain number will undergo spontaneous decay, falling back into the ground state and emitting photons in the process. The warmer the atmosphere the higher the rate of emission -- for the same reason a hot iron will glow more brightly the hotter it gets. The main difference is that with a greenhouse gas like CO2 matter is able to emits only in a few bands."

It is spontaneous decay. The molecules have no memory of how long they have been in a given state of excitation, therefore if a certain percentage are in a given state of excitation at any given time then a certain percentage will undergo spontaneous decay due to the emission of radiation over a given period of time.

Maxwell, as an aside that has to be the most appropriate name for this comment. Since de-excitation is an energy loss process just about every collision can de-excite a vibrationally excited greenhouse gas molecule. However, the distribution of collision energies is the Maxwell-Boltzmann distribution which means that while most collisions do not have enough energy to vibrationally excite one of the greenhouse gas molecules, a few in the high energy tail do. The result is an equilibrium. As Eli wrote elsewhere

While most understand how radiation is converted into heat the reverse process is more subtle. As you said, greenhouse gas molecules absorb IR radiation. When they do this, they move to a higher energy quantum state (vibration rotation). However, this excess energy rapidly is converted into translational energy by collision with other molecules (N2, O2, etc) Essentially NONE of the absorbed energy is re-radiated from the excited molecule before it is quenched otherwise we could not say that the distribution of energy among all the molecules (and in particular the greenhouse gas molecules) was thermal. By this we mean that the distribution of energy in each of the modes of motion, translation, vibration and rotation, is characterized by the same temperature.

OTOH, thermal collisional energy is high enough that for a few collisions at atmospheric temperatures a small fraction of the greenhouse gas molecules are constantly being vibrationally/rotationally excited by collisions with the O2 and N2, etc. Of course, as many as are excited, are de-excited per second. Still, we can regard this as maintaining an equilibrium population of excited molecules (same number, but each molecule cycles in and out constantly), and on average a constant number of these excited molecules radiate per second. It is this back and forth that maintains a thermal equilibrium in the atmosphere.

So now there are two contradictory notions going on in this thread it seems to me.

1) Thermalization of the absorbed IR light from greenhouse gases causes the ambient temperature of a gas to increase because there is more energy in the translational motion of mostly homonuclear diatomic molecules.

2) (thanks to Timothy) The temperature of the lower troposphere (where most of the IR absorption by CO2 is happening) has to increase to a point where it can emit as much radiation as it takes in.

I think I believe 1) more than 2) though because I don't think that Planck feedback works on a layer by layer basis in the atmosphere, though I could be mistaken. If Planck feedback does work that way, we're back to explaining how homonuclear diatomic molecules can emit radiation in the far IR and mircowave region of the EM spectrum, which I'm 99% sure they cannot do.

It seems to me that if collisions are thermalizing the IR absorbed by GHG's, then the only way get balance at the TOA would be from excess emission from higher layers of the atmosphere, which we do see.

I'd guess it's some linear combination of these two proposed processes. Some the energy gets thermalized while some of it is also emitted directly by the GHG's themselves in random directions. I wonder if there is a way to take the satellite data and break it down into these two physical processes explicitly.

Maxwell,Think about it. What happens as we move higher in the atmosphere? The gas becomes less dense and colder--both of which favor photoemission over collisional relaxation. This is why we get an emission spectrum characteristic of a particular altitude/temperature.

Eli is right. Think of it as an equilibrium. You've got ~10^15 ions per cc even high in the atmosphere.

Whatever else may be true, an “Explanation” like Curry’s does not add much (except maybe confusion) to the conversation:

"Then through the equipartition of energy, the absorption of radiation causes the molecule to move faster and bump into the other molecules like N2, O2, and make them move faster. …”

It may not have been her intention, but that sure reads like "the absorption of radiation directly causes the molecule to move around [ie, from place to place] faster"

Granted, one way to intepret “move faster" is “ vibrate more", since absorption of IR radiation causes a CO2 molecule to vibrate and vibration is a form of movement, after all.

But the second part of the very same sentence "...and bump into the other molecules" makes it pretty clear that Curry’s “movement” does not refer to vibration but, rather, to translation of the molecule.

In a gas at atmospheric pressures (air in this case), where the molecules are very far apart except during collisions, vibration does not cause one molecule to "bump into the other molecules", at any rate.

So, the second part of Curry's statement implies that her full statement should actually be read as "the absorption of radiation causes the molecule to move from place to place faster and bump into the other molecules like N2, O2, and make them move faster."

In other words, if we are to accept Curry's explanation,somehow ( through the "magic" of equipartition of energy?) the energy of vibration of the molecule (induced by absorption of IR radiation) is being converted into energy of translation -- and this is occurring before the molecule collides with other molecules (!)

Maxwell wrote, "2) (thanks to Timothy) The temperature of the lower troposphere (where most of the IR absorption by CO2 is happening) has to increase to a point where it can emit as much radiation as it takes in."

Maxwell, I didn't say "lower troposphere." And what matters in terms of radiation balance is TOA "Top of Atmosphere."

For equilibrium to exist for the Earth as a whole the rate at which energy leaves the system has to equal the rate at which energy enters the system. But that doesn't say how the energy gets to where it is finally radiated to space. Although it varies depending upon the part of the spectrum, on average that is about 5.5 km up.

Below that moist air convection plays a rather important role, thermals less of one. But neither moist air convection nor thermals can get energy from the atmosphere to space. For that you need radiation. Neither moist air convection nor thermals can exist in a vacuum. Radiation can.

However, when you raise the level of greenhouse gases in the atmosphere in those parts of the spectrum where they are active you reduce the rate at which radiation escapes to space. Given that the atmosphere has become optically thicker, the radiation is only able to escape to space higher up where the atmosphere is colder. The effective radiating temperature of the Earth (the temperature it appears to be from space) falls.

Now the rate at which the atmosphere radiates is proportional to the temperature taken to the fourth. So this higher layer from which photons finally escape will have to warm up if energy is to leave the system at the same rate as before, and given a constant lapse rate due to convection (rate at which temperature falls with increasing altitude) this will imply a warmer surface.

And yes, I touch on this at my webpage -- and like Eli the fact that at a given temperature a certain percentage of the population of CO2 molecules will be in an excited state at any given time, and therefore carbon dioxide molecules will be undergoing radiative decay at a specific rate. I just don't state it as technically -- or with anywhere near as much understanding backing me up.

If at any point Eli and I contradict one another -- at least in this area and probably anything related to physics or chemistry -- you should go with what Eli says. He's got the technical background and I don't. Oh, and let me know when he and I actually do contradict one another. I'll see if he can straighten me out.

Anyway, at the webpage check out Iain Stewart's experiment in which higher levels of carbon dioxide in a tube reduce the rate at which thermal radiation from a candle makes it from one end of the tube to the other -- as seen by an infrared camera. This implies that radiation is being absorbed by the gas. This implies that the gas has to warm up -- until the rate at which radiation is emitted is the same as before.

The same thing happens with our atmosphere. You see my avatar? As I explain, it is the product of satellite imaging in the infrared spectrum in the radiation band around wavelength of 15μm with a wavenumber of about 667 (1/cm). This the part of the spectrum in which the bending mode of CO2 operates.

The dark red in the satellite image? That is where higher levels of carbon dioxide are reducing the rate at which radiation in this part of the spectrum is escaping to space. Essentially you are seeing the greenhouse effect in action.

The reason for those red areas? Well, the two large regions -- which you can likewise see in my avatar -- are from large plumes of carbon dioxide coming off of the densely populated, industrialized West and East coasts of the United States. The large band in South America? The use of fire to clear jungle for farmland.

But I have included satellite images of other parts of the globe. The carbon dioxide coming off of Europe? Industry -- and forest fires from that year. South Africa? The liquification of coal into synthetic oil. Australia? Coal-based power plants.

Given our understanding of the physics and the technology that this understanding makes possible we can actually see these things. We will soon be able to see things in even greater detail with the launch of the Orbiting Carbon Observatory OCO-2 -- due to be launched in February 2013.

I think I figured out a better way to explain what is going on than thinking about turnstiles.

We have the atmosphere up above the earth and it is sitting at some given temperature (which doesn't actually change all that much in the course of the experiment on the scale of things). The main reason that it is at that temperature is not radiative at all - it's thermal convection between the ground and the other parts of the atmosphere.

When we add some CO2 to the atmosphere, it is better at absorbing the upwelling radiation. This is true, but not the main issue. It is also better at *emitting* radiation than it was (because of the second law of thermodynamics, which requires that if a body is good at absorbing, it is also good at radiating). Now the earth is getting its radiation from the sun, but also from the downwelling radiation from the atmosphere. This new source of energy wasn't there before, and so the earth gets hotter.

Yes, that is true. The point is that if we're trying to focus on why the surface gets hotter, the easiest thing to see is not the blocking of the outbound radiation, but the addition of the downwelling radiation. The temperature of the atmosphere is determined by the dry (or moist) adiatbat, which has to do with stability under convection. So while it's true that the CO2 absorption does block the outgoing radiation, you can most easily see what is warming the surface a different way.

Mitch, near the surface pretty much whatever bands carbon dioxide would be active in are already saturated by water vapor. Carbon dioxide works because it plays an integral role where the role of water vapor is negligible.

Therefore arguing strictly on the basis of backradiation at the surface would leave you wide open to "skeptic" argument that carbon dioxide has virtually no effect on surface temperature given the saturation at the surface. Furthermore they could cite material that is true but highly selective.

Even if the people you are trying to convince don't raise the issue with you someone might very well raise the issue with them later on. Or perhaps it will be someone who already basically agrees you who is listening to your discussion then tries your argument in the middle of a discussion or debate in some other forum. By oversimplifying you've handicapped them.

Timothy Chase, so how does the surface warm then? Could it be that not all CO2 bands are the same as H2O bands and the bands are in any case not lines but bell curves and the area under the sides of the bell away from the center become more important with increasing concentration, and by the way there are feedbacks: more water vapor too.

Pete Dunkelberg wrote, "Timothy Chase, so how does the surface warm then? Could it be that not all CO2 bands are the same as H2O bands and the bands are in any case not lines but bell curves and the area under the sides of the bell away from the center become more important with increasing concentration, and by the way there are feedbacks: more water vapor too."

So that you aren't relying entirely upon me, here are a few pieces -- particularly at Real Climate and Rabett Run -- that I would strongly recommend.

However, for the moment lets focus on just two passages from "A Saturated Gassy Argument."

First:

"In the infrared spectrum, the main bands where each gas blocked radiation overlapped one another. How could adding CO2 affect radiation in bands of the spectrum that H2O (not to mention CO2 itself) already made opaque?" (Spencer Weart, A saturated Gassy Argument)

Essentially he is pointing to the same problem I have with attempting to explain the warming of the surface simply in terms of backradiation. The the atmosphere near the surface is already about as opaque as it is going to get to infrared radiation, at least in the part of the spectra in which CO2 operates.

Second, a somewhat longer passage that further indicates the nature of the problem as well as the solution:

"Among other things, the new studies showed that in the frigid and rarified upper atmosphere where the crucial infrared absorption takes place, the nature of the absorption is different from what scientists had assumed from the old sea-level measurements. Take a single molecule of CO2 or H2O. It will absorb light only in a set of specific wavelengths, which show up as thin dark lines in a spectrum. In a gas at sea-level temperature and pressure, the countless molecules colliding with one another at different velocities each absorb at slightly different wavelengths, so the lines are broadened and overlap to a considerable extent. Even at sea level pressure, the absorption is concentrated into discrete spikes, but the gaps between the spikes are fairly narrow and the "valleys" between the spikes are not terribly deep." (Spencer Weart, A saturated Gassy Argument)

You note that the bands are not continuous but consist of lines. Further, you note that even though the bands of carbon dioxide and water vapor overlap, the lines are in different places -- so carbon dioxide and water vapor aren't necessarily blocking radiation in exactly the same part of the spectrum.

However, while this continues to be true near the surface, higher concentrations lead to saturation further and further from the peaks -- the centers of the lines and increased pressure leads to pressure broadening. The regions over which absorption does not take place (what he refers to as "the valleys") become very narrow. Both concentration and pressure result in greater overlap between the spectra of carbon dioxide and water vapor near the Earth's surface, and as water vapor is far more abundant, near the Earth's surface the effects of carbon dioxide and increased levels of carbon dioxide are rather negligible -- as its roughly equivilent to doubling the amount of a minute part of the water vapor.

But at higher altitudes the density of water vapor falls quickly due to the fact that it is precipitable. The atmosphere has an e-folding distance (distance over which density decreases by a factor of ~2.7) of roughly 8 km. The same is true of cabon dioxide and so we call it "well-mixed". With water vapor the e-folding distance is more like 1.5-2.0 km.

Furthermore, at lower pressures, while the total absorption remains the same (see "Pressure Broadening" by Eli Rabett, JULY 05, 2007 and "Part II: What Ångström didn't know"by Raymond T. Pierrehumbert, 26 June 2007) the region over which the absorption from an absorption line takes place narrows. Consequently there is less overlap between the spectra of carbon dioxide and water vapor and the effects of increased carbon dioxide become more pronounced.

And what matters most is what takes place not at the surface but where radiation finally escapes to space. By increasing the concentration of carbon dioxide you increase the height at which it finally escapes to space. But this implies that it is escaping from a colder layer. In accordance with the Stefan Boltzmann law (that I mentioned earlier in the same context, actually) the rate at which an object -- or the atmosphere -- radiates is proportional to the absolute temperature taken to the fourth power. Consequently you reduce the rate at which radiation is radiated into space.

This results in an imbalance between the rate at which energy enters the system and the rate at which energy leaves the system. Consequently thermal energy builds up in the atmosphere. The lower layers radiate as before but the higher layers where radiation is now finally escaping from have yet to warm up. And it is only by their warming up that the balance between energy entering the system and energy leaving the system may be re-established.

As the higher layers warm up this will reduce the temperature differential between those higher layers and the lower layers closest to them. This implies increased backradiation between the higher layers and lower layers just below them, reduced convection and so on. Essentially you have added a blanket reducing the rate of heat transfer to space. So the neighboring lower layers warm, reducing the temperature differential between them and the layers just beneath them. The atmosphere warms from the outside in.

As Ray Pierrehumbert states,

"The way the greenhouse effect really works is that adding CO2 reduces the infrared out the top of the atmosphere, which means the planet receives more solar energy than it is getting rid of as infrared out the top. The only way to bring the system back into balance is for the whole troposphere to warm up. It is the corresponding warming of the low level air that drags the surface temperature along with it — an effect left entirely out of Plass' calculation."

Perhaps Eli will allow a confused rodent to cross post from Skeptical Science on the related issue of stratospheric cooling:

1) The stratosphere features very little convection, so radiative heat transfer dominates2) The stratosphere is heated by UV absorption by ozone and also somewhat by IR absorption by CO2.3) Due to higher CO2 levels, more IR is absorbed in the troposphere, so less in the stratosphere, resulting in cooling of the stratosphere as CO2 rises.

Is this correct ?

It begs one question, which I think needs a full heat transfer model to answer:

Consider a thought experiment with CO2 at zero. There is no CO2 IR absorption either in the troposphere or stratosphere. Now allow CO2 to rise.

Initially, despite increased (from zero) tropospheric CO2 IR absorption, there will also be increased stratsopheric absorption (by definition, as it was zero)

So we initially expect a rise in stratospheric temperature, peaking at some level of CO2, then falling as increased tropospheric absorption blocks stratospheric IR absorption by CO2.

Is this correct ? And if so what's the CO2 level at which stratospheric temperatures start to fall ?

I see what you're talking about - point well taken. In which case I still don't see how a turnstile analogy works. The reason is just that the outgoing radiation is coming from the top of the atmosphere rather than the bottom, and the top of the atmosphere is colder than the bottom.

A turnstile analogy makes it sound like the energy is passed via radiation layer by layer through the atmosphere.

"A turnstile analogy makes it sound like the energy is passed via radiation layer by layer through the atmosphere."

Well, there are things that can be done. For example, the turnstile analogy might still work -- if I suppose you treat moist air convection as some sort of escalator or moving sidewalk. But then things break down again when you realize for example that thermalization or "quenching" implies that you can't track an individual packet of energy from the surface to space.

Thermalization essentially implies that each time a photon is absorbed then energy that made up that photon becomes distributed between a large number of molecules and then new photons come into being made up of bits of the energy that what part of the individual photons that preceded them. A bit like if you were to put people through blenders every few floors as they made their way to space -- and kept repackaging entirely new people along the way.

I am not sure that any one analogy does that well, greenhouses, bath tubs, blankets, pinball machines, the scattering of light by fog. They all break down at one point or another. But they are useful, and once they have been used you can point out their limitations, using their limitations as a further means of illumination.

Likewise backradiation certainly can be used to illustrate the greenhouse effect -- if you point out that just as the surface receives backradiation from the layer of atmosphere above it -- and that what ultimately matters is the backradiation from the "top of the atmosphere" where carbon dioxide plays its central role. Then the backradiation becomes a stepping stone of understanding, like the analogies.

And I would also keep in mind the fact that we have performed detailed measurements of the absorption spectra of carbon dioxide and water vapor, there is that YouTube video of Iain Stewart demonstrating how carbon dioxide absorbs infrared radiation at different pressures, temperatures and concentrations.

We have the satellite images showing how carbon dioxide reduces the amount of infrared radiation making its way to space. In essence photographic proof of the greenhouse effect in action.

Furthermore, many of the principles that form the basis for our understanding of the role of carbon dioxide in the greenhouse effect are the very same principles underlying our technologies that we rely on every day. These include tunnel diodes lasers, nuclear magnetic resonance imaging, microwave ovens. They include the infrared imaging devices that get used by missiles and fighter planes. In a very important sense our understanding of the greenhouse effect gets tested every time we use any device that relies on the same physical principles. And finally, I would remind them that we have been familiar with carbon dioxide's ability to absorb infrared radiation since the 1800s, and that it was proposed as far back as the early 1860s that raising the concentrations of carbon dioxide in the atmosphere would result in higher temperatures.

Timothy Chase, Thanks! It is not every day that one can post a question online and get a good, detailed answer. Muchas gracias!

Very Tall Guy, I'll try your thought experiment. I think ozone interacts some with IR, but not enough to cool itself as much as can happen with a little help. (The stratosphere is not nearly hot enough to radiate UV, thankfully!) Now add CO2. It does not directly pick up more energy from UV, but it picks up energy from the hot ozone which the ozone got from UV and radiates IR in all directions, cooling the stratosphere.

Eli, it's a Pinball Machine! A packet of energy bounces around through the gates and maybe makes it out.

I'm thinking that most of the thermal radiation makes it's way to the top of the atmosphere is 70% (earth radiation budget, http://eosweb.larc.nasa.gov/EDDOCS/whatis.html). Better than a pinball machine.

Chandrasekhar provided the equations of radiative transfer to calculate the movement of radiation up and down in an atmosphere. Used for stellar atmospheres as well.

A very interesting article is by Lacis et al from GISS in Science, 15 Oct 2010, p 356. They modeled what would happen if all the CO2 was removed from the air; the planet would freeze solid in 50 years except for water at the equator receiving direct sunlight. The water vapor in the air cannot hold the livable temperature on its own. The article is also a good summary of the case for anthropogenic global warming. I recommend it for those with a strong background.

The earth, as a whole that would be measured at the top of the atmosphere, is not increasing in temperature. The lower troposphere is increasing in temperature. Therefore, if we're going to start invoking the Stefan-Boltzmann equation to understand why temperature increases in response to increasing to concentrations of GHG's, we have to be discussing the lower troposphere.

One of ways we know the warming we've measured is from an increased greenhouse effect is the fact that the higher altitude layers in the atmosphere have cooled. That happens because energy that would be transferred to those layers is being absorbed and thermalized at lower altitudes.

So the TOA radiation flux can stay exactly the same, implying to net change in temperature of the earth, as whole, doesn't change. The temperature difference between the layers of the atmosphere changes, however.

In fact, the measured change in TOA radiation flux is 1% plus/minus 0.5% to 1%, depending on the specific measurement. This change in flux is also not only dependent on the greenhouse effect. So even though there has been measurable change in the temperature of the lowest layer of the atmosphere, especially in the last 30 years, that change in tropospheric temperature does not correspond to a significant change in the TOA radiation flux.

... you will notice that they show radiative forcing as taking place at the tropopause first, a cooling of the stratosphere second, warming in the upper troposphere third, and then warming at the surface and final equilibrium. A bit oversimplified, no doubt. But there is a great deal of truth to it nevertheless. The troposphere near the surface is already optically thick. Increasing CO2 concentrations there won't have much of any effect.

Raising CO2 concentrations where higher concentrations are sufficient to make an optically thin layer optically thick will have an effect. It will shift the effective radiating layer to a higher altitude. That higher altitude will be cooler. In accordance with Kirchoff's law the radiation emitted by that layer will be a function of the temperature and makeup of that layer and otherwise independent of the radiation that it absorbs. So the temperature of that layer will have to rise if it is to emit radiation like the earlier effective radiating layer. As it is initially radiating less radiation the stratosphere will cool.

With sunlight and albedo remaining constant the rate at which thermal radiation enters the system will remain the same, but with a cooler effective radiating layer the rate at which thermal radiation escapes has decreased. Therefore there is a radiation imbalance. Thermal energy will accumulate in the system until it is emitting thermal infrared radiation at the same rate as before.

The new effective radiating layer at the higher altitude warms. When a higher layer warms the rate at which heat is transferred from the warmer layer below it will decrease, warming that layer until the difference in temperature between the two layers (temperature gradient) is roughly what it was before. But as that lower layer warms this will decrease the difference in temperature between it and the warmer layer directly below it. The troposphere will warm from the top down.

... and the links I gave in an earlier comment here -- and you might find some value in the two comments I made immediately after that -- which covered much the same material I just covered now. (But I try not to duplicate things too much, so I believe you will find more to learn there.)

... and the links I gave in an earlier comment here -- and you might find some value in the two comments I made immediately after that -- which covered much the same material I just covered now. (But I try not to duplicate things too much, so I believe you will find something more of value there.)

"As it is initially radiating less radiation the stratosphere will cool."

Everything else in your post i agree with, except for the reason for stratospheric cooling with raised CO2. The stratosphere is a net emitter to the troposphere, the reason being, CO2 acts as a net emitter at the path lengths found above the troposphere. It emits more than it absorbs, effectively meaning it transmits energy through radiation.

"O3 causes a net radiative heating of around 15Wm^2, which is compensated by the net cooling due to CO2 & H2O. The solar and long wave absorption by O3 is almost equal to the CO2 & H2O long wave absorption. The long wave absorbed by O3 is, however, nearly a factor of two larger than emission, where as for CO2 & H2O the long wave absorption is nearly a factor of two smaller than emission."

So by increasing the number of CO2 molecules per volume, you are increasing the rate at which energy can be moved out of the stratosphere via radiation, with loses of setting gains. This is the main reason for stratospheric cooling due to raised co2.

Joe, we have had something like this before. I don't think it was deliberate but a bug in Blogspot. If it behaves anything like the last time your comment will re-appear after a while. Anyway, I am experiencing the same thing. I have posted part II of II twice and it has disappeared both times.

... and the links I gave in an earlier comment here -- and you might find some value in the two comments I made immediately after that -- which covered much the same material I just covered now. (But I try not to duplicate things too much, so I hope you will find something more of value there.)

Some Professor S has reported the same problem. Hope you don't mind but I commented that you are experiencing it as well. He has been having it for two days now -- hoped that things would correct themselves, but they haven't so far and so he created a thread where Google tracks defects for Blogger.

For me reading what Curry has to say would be a race between boredom and depression. But plenty of interesting stuff gets said by those who have the stomach for it. I will look for it over here though. Oh, and the bit about the airport? Took me a moment.

I've found a solution to the depression that results from reading about Judy's slow descent into utter irrelevance. I don't read about it. I can honestly say that I've never found anything she had to say particularly enlightening. There was never anything about which I said, "Oh, that's how it works!" Spencer used to be somewhat educational, but has descended further and further into obfuscation and epicycles of complexity. McI was a one-trick pony and has nothing to say, and Lindzen remains entranced by his beautiful, mythical Iris. Not much science being done on the denialist side.

I've not really looked at that blog before - there's some truly weird stuff that seems to pass un-noticed, e.g."Water has no bearing to climate change: H2O is compressed gases that developed an alliance with salt. In the past it was much saltier than today as centrifugal force was faster and would have generated far more evaporation than today if not for the increased density. Salt changes on the surface of the oceans are directly caused by atmospheric pressure increase. With increased salt on the surface of the oceans, there is more solar reflection and less solar penetration in the oceans."

Hm, is this any help?http://docs.google.com/viewer?a=v&q=cache:ijYRgr-9OP4J:article.pubs.nrc-cnrc.gc.ca/ppv/RPViewDoc%3Fissn%3D1480-3291%26volume%3D52%26issue%3D8%26startPage%3D1436+nitrogen+vibrational+level+stratosphere&hl=en&gl=us&pid=bl&srcid=ADGEESgPyunBaMkQZGtdacn3wG3xFYUk_SQUtG42cMVxMDNKBDBjeYOtG4JkimyvOcuR0Iup8A8eFX7WXJNTxNuoToE7kJOUTEFM_LWHdx9EmluP4VngywwwMmvapBcQDKzlCe1EgHbP&sig=AHIEtbRL54_MNvYSmO-UO9hhw1Y-xS7aIQ

The turnstile analogy says that if you put more turnstiles in, then more energy will pass. All IR absorber/emitters are responsible for cooling the surface, which would not happen if there were no IR absorber/emitters. Isothermal earth would obviously and unchallengably be warmer as core heat is distributed equally.

Of course the turnstile works in both directions. But net heat energy is only queuing up on the hot side. If there are no turnstiles, there is no cooling. The turnstiles are frictionless, reversible and unmotorized.

Rabett Run

Subscribe Rabett Run

The Bunny Trail By Email

Contributors

Eli Rabett

Eli Rabett is a not quite failed professorial techno-bunny, a chair election from retirement, at a wanna be research university that has a lot to be proud of but has swallowed the Kool-Aid. The students are naive but great and the administrators vary day-to-day between homicidal and delusional. His colleagues are smart, but they have a curious inability to see the holes that they dig for themselves. Prof. Rabett is thankful that they occasionally heed his pointing out the implications of the various enthusiasms that rattle around the department and school. Ms. Rabett is thankful that Prof. Rabett occasionally heeds her pointing out that he is nuts.